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Simplifying 3t2 + -8t + -3 = 10t2 + 16t + 6 Reorder the terms: -3 + -8t + 3t2 = 10t2 + 16t + 6 Reorder the terms: -3 + -8t + 3t2 = 6 + 16t + 10t2 Solving -3 + -8t + 3t2 = 6 + 16t + 10t2 Solving for variable 't'. Reorder the terms: -3 + -6 + -8t + -16t + 3t2 + -10t2 = 6 + 16t + 10t2 + -6 + -16t + -10t2 Combine like terms: -3 + -6 = -9 -9 + -8t + -16t + 3t2 + -10t2 = 6 + 16t + 10t2 + -6 + -16t + -10t2 Combine like terms: -8t + -16t = -24t -9 + -24t + 3t2 + -10t2 = 6 + 16t + 10t2 + -6 + -16t + -10t2 Combine like terms: 3t2 + -10t2 = -7t2 -9 + -24t + -7t2 = 6 + 16t + 10t2 + -6 + -16t + -10t2 Reorder the terms: -9 + -24t + -7t2 = 6 + -6 + 16t + -16t + 10t2 + -10t2 Combine like terms: 6 + -6 = 0 -9 + -24t + -7t2 = 0 + 16t + -16t + 10t2 + -10t2 -9 + -24t + -7t2 = 16t + -16t + 10t2 + -10t2 Combine like terms: 16t + -16t = 0 -9 + -24t + -7t2 = 0 + 10t2 + -10t2 -9 + -24t + -7t2 = 10t2 + -10t2 Combine like terms: 10t2 + -10t2 = 0 -9 + -24t + -7t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 24t + 7t2) = 0 Factor a trinomial. -1((3 + t)(3 + 7t)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + t)' equal to zero and attempt to solve: Simplifying 3 + t = 0 Solving 3 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + t = 0 + -3 t = 0 + -3 Combine like terms: 0 + -3 = -3 t = -3 Simplifying t = -3Subproblem 2
Set the factor '(3 + 7t)' equal to zero and attempt to solve: Simplifying 3 + 7t = 0 Solving 3 + 7t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 7t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7t = 0 + -3 7t = 0 + -3 Combine like terms: 0 + -3 = -3 7t = -3 Divide each side by '7'. t = -0.4285714286 Simplifying t = -0.4285714286Solution
t = {-3, -0.4285714286}
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